**Variations in the work function of doped single- and few-layer graphene assessed by Kelvin probe**

**force microscopy and density functional theory**

D. Ziegler,1,*P. Gava,2J. G¨uttinger,3F. Molitor,3L. Wirtz,4M. Lazzeri,2A. M. Saitta,2A. Stemmer,1
F. Mauri,2_{and C. Stampfer}3,5

1* _{Nanotechnology Group, ETH Zurich, 8092 Zurich, Switzerland}*
2

*3*

_{Universite Paris 6/7, CNRS IPGP, 75015 Paris, France}

_{Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland}4_{Institute of Electronics, Microelectronics, and Nanotechnology (IEMN), Department ISEN, CNRS-UMR 8520, B.P. 60069,}

*59652 Villeneuve d’Ascq Cedex, France*

5_{JARA-FIT and II, Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany}

(Received 3 January 2011; revised manuscript received 25 April 2011; published 30 June 2011) We present Kelvin probe force microscopy measurements of single- and few-layer graphene resting on SiO2

*substrates. We compare the layer thickness dependency of the measured surface potential with ab initio density*
*functional theory calculations of the work function for substrate-doped graphene. The ab initio calculations*
*show that the work function of single- and bilayer graphene is mainly given by a variation of the Fermi energy*
with respect to the Dirac point energy as a function of doping, and that electrostatic interlayer screening only
becomes relevant for thicker multilayer graphene. From the Raman G-line shift and the comparison of the Kelvin
*probe data with the ab initio calculations, we independently find an interlayer screening length in the order of*
four to five layers. Furthermore, we describe in-plane variations of the work function, which can be attributed to
partial screening of charge impurities in the substrate, and result in a nonuniform charge density in single-layer
graphene.

DOI:10.1103/PhysRevB.83.235434 *PACS number(s): 73.22.Pr, 74.20.Pq, 71.15.Mb, 63.22.Rc*

**I. INTRODUCTION**

Carbon nanomaterials and in particular single-layer
graphene, a truly two-dimensional (2D) solid with unique
electronic1,2 _{and mechanical properties,}3 _{attract increasing}
interest, mainly due to possible applications in high mobility
nanoelectronics,4–7_{and sensor technologies.}8 _{Since graphene}
only consists of surface atoms, a number of new schemes for
local doping,9 surface functionalization,10 gas sensing, and
atomically thin nanoelectronic circuits11,12become accessible.
In this context, the graphene-substrate interaction and, more
generally, the interaction between graphene and its
environ-ment plays a crucial role as it limits the intrinsic electron
mobility in graphene.13,14 The interaction with the substrate
and environment is associated with the formation of disorder
potential which, in turn, reduces mobilities, limits energy gaps
in nanoribbons15,16_{and bilayer graphene,}17_{and has significant}
impact on the noise level in graphene devices in general.18
Detailed studies elucidated substrate-induced electron-hole
puddles,19 doping domains in graphene,20 and local
quan-tum capacitances.21 _{Kelvin probe microscopy experiments}
on single- and few-layer graphene have been reported.22,23
*Datta et al.*22_{discussed the surface potential as a function of}
layer thickness and compared their result with Thomas-Fermi
theory accounting for interlayer screening of the system.
*Yu et al.*23 have shown that the work function of
single-and bilayer graphene can be widely tuned by changing the
carrier density. They explain the doping-induced change in
the work function using the Fermi level shift obtained from
band structure calculations. Here, we report on Kelvin probe
force microscopy (KFM) in ambient conditions of single-,
bi-, and few-layer graphene resting on SiO2. We compare
*the KFM data with ab initio density functional theory (DFT)*

calculations of the work function for substrate-doped (i.e.,
surface doped) graphene. The calculations take into account
two effects: the substrate-induced charge on the system, and
the interlayer screening, i.e., the charge redistribution among
the layers. In particular, our calculations show that for
single-and bilayer graphene the work function is mainly determined
by the Fermi level shift with respect to the Dirac point, i.e.,
the substrate-induced charge, which confirms the theoretical
*model used by Yu et al.*23 _{The effect due to the interlayer}
screening becomes important for multilayer graphene thicker
*than bilayer. Furthermore, we compare our results with Raman*
G-line shifts, and discuss substrate-induced variations of the
work function, which provide insight into the disorder potential
at elevated doping levels in single-layer graphene.

This paper is organized as following: In Sec. II, we
describe the experimental setup and present Kelvin probe
measurements as well as Raman spectroscopy data. In
Sec. III*, we introduce the ab initio DFT approach for*
calculating the work function as function of the number of
graphene layers. Finally, we compare the experimental Kelvin
*probe data with the ab initio DFT calculations in Sec.*IV.

**II. SETUPS AND MEASUREMENTS**

Kelvin probe measurements are performed under ambient
conditions using a multimode microscope (Veeco) operated
by a Nanonis SPM controller (SPECS). First, the
topogra-phy of each scan line is recorded using tapping mode for
distance control. In a second pass, at a constant distance
from the sample (lift height= 5–50 nm), we perform KFM
using amplitude modulation (AM-KFM). The frequency of
*the applied electrical modulation, Vac*, is matched to the

-0.5 -1.5 -1 -2 Vac Vdc Vdc (V) Photodiode Laser Cantilever 3.2 nm

## SiO

## SiO2

## 1LG

## 1LG

## 6LG

## 6LG

Z Kelvin Probe ControllerFIG. 1. (Color online) Schematic illustration of the Kelvin probe force microscopy setup used to investigate graphene flakes resting on SiO2. In the three-dimensional rendering of the topography brighter

areas indicate higher recorded contact potential difference (V*dc*) (see

scale bar). A lower V*dc* i.e. higher work function is recorded over

areas of single-layer (1LG) than six-layer (6LG) regions.

cancels electrostatic forces by adjusting the tip bias voltage,

*Vdc*, until zero amplitude is reached.24,25 *Here, Vdc*

compen-sates for potential differences between tip and sample, and if
*the tip work function *tipis known, the work function of the
*sample is given by s= *tip*− eVdc*. The local variations of

the work function, however, can be expressed independent of

_{tip}*by S=−eVdc*. An example of such a measurement

is shown in Fig.1, where the topography is mapped onto the
*third dimension (z-axis) and the recorded surface potential*
*(Vdc*) is color coded. Figures2(a)and 2(c) show topography

and Kelvin probe measurements of an isolated graphene flake consisting of single-layer (1LG) and bilayer (2LG) regions [see labels in Figs.2(a)and 2(c)]. The samples were obtained by mechanical exfoliation of bulk graphite, as described in Refs.4

and26. The Raman data as shown in Fig.2(b)are acquired by
using a laser excitation of 2.33 eV through a single-mode
optical fiber, whose spot size is limited by diffraction to
∼400 nm. The width and shape of the 2D Raman line [see,
e.g., Fig.3(c)] confirm the number of graphene layers26,27_{and}
single-layer regions can be well distinguished from bilayer
regions in the full width at half maximum (FWHM) of the 2D
line as shown in Fig.2(b)(see areas separated by white dotted
line).

In Fig.2(d), we show a histogram analysis of the acquired
Kelvin probe data over an area enclosing the graphitic flake
as indicated in Fig. 2(c) (see black dashed line). Gaussian
fitting reveals the average values of the measured surface
potentials on the single- and bilayer graphene regions [see
labels in Figs. 2(a) and 2(d)], which reproducibly show
*a difference of V _{dc}*(2−1)≈ 66 mV [Fig. 2(d)]. The strong
scattering, i.e., the width of the distribution of the surface

*potential on the single- and bilayer region of δVdc*≈ 25 mV

can most likely be attributed to an inhomogeneously charged
background [see, e.g., right edge of Fig.2(c)]. The isolated
graphitic flake has been charged by bringing the metallic tip in
*electrical contact and applying a tip voltage (Vdc*) of either 1 V

360 380 400 420 440 460 480
(a)
(d)
(b) (c)
Topography
**1LG**
**2LG**
**2LG**
**1LG**
**1LG**
**2LG**
Raman
Histogram
Kelvin Probe
**FWHM**
** 2D**
(e)
(f)
(V )dc
**33cm-1**
**2 µm**
V_{dc} (mV)

Pixel Frequency (arb.units)

240 mV 380 mV 620 mV 950 mV 380 mV 1330 mV 2060 mV 380 mV 2440 mV

FIG. 2. (Color online) (a) AFM topography image of an isolated
graphitic flake consisting of single- and bilayer regions (see labels
and white dashed line along the boundaries), highlighted and proved
by a confocal Raman map (b) showing the FWHM of the 2D
Raman line. (c), (e), and (f) Kelvin probe data, i.e., surface potential
measurements. (d) Histogram analysis of the acquired Kelvin probe
data [taken from the area enclosed by the black dashed line shown in
panel (c)]. The two peaks can be attributed to the single- (1LG) and
*bilayer (2LG) regions and a surface potential difference of V _{dc}*(2−1)≈
66 mV is observed.

[Fig.2(e)] or 2 V [Fig.2(f)]. Since the highly doped Si substrate
has been grounded, this corresponds to an added charge carrier
*density of roughly n≈ αVdc, where α= 7.2 × 10*10 cm−2

V−1 (Ref. 4*), leading to n≈ 7.2 × 10*10 _{cm}−2 _{and n}_{≈}
*1.4*× 1011 _{cm}−2_{, respectively. In Figs.} _{2(c)}_{,} _{2(e)}_{, and} _{2(f)}_{,}
the relative color scale is kept constant and just the overall
charge dependent offset has been adapted (see color scales).
*Interestingly, the surface potential difference Vdc*(2−1) is—

within the error bars—not affected by the overall charging of the flake, indicating that such small charging and in particular charge rearrangements across single- and bilayer graphene regions do not strongly alter the work function difference

(2−1)_{S}*= −eV _{dc}*(2−1)

*, which is in agreement with ab initio*calculations as shown below.

### c

### b

### d

### e

### f

### a

**I (a.u)**

**I (arb.u)**

**6LG**

**1LG**3.2 nm I(arb.units) I(arb.units) (a) (b) (c) (d) (f) (e)

FIG. 3. (Color online) (a) 2D-FWHM Raman map of a few-layer graphene flake with sections ranging from six layers down to a single layer (taken before electrically contacting the flake). (b) Raman map of the G-line intensity where (c) and (d) are the full Raman spectra taken on two different region [see labels in (b)]. (e) The AFM topography (with inset indications of the number of layers) and (f) Kelvin probe image of the same flake after contacting [image corresponds to the dashed square in panel (a)]. The labeled boxes therein relate to Fig.6.

in Fig. 3(b)]. Figure3(c), for example, shows a single-layer
spectrum with a narrow 2D line (and no D line), whereas
Fig.3(d)shows a Raman spectrum of a six-layer-thick region
confirmed by atomic force microscope (AFM) measurements.
Topography and Kelvin probe measurements of this very same
flake are shown in Figs. 3(e) and 3(f). The different layer
*dependent surface potential values Vdc*can be clearly identified

in Fig.3(f)[see also numbered labels in Fig.3(e)]. We observe
*that the surface potential Vdc* increases with increasing layer

thickness, which predicts p-doping of the sample.28 _{For the}
surface potential difference between the single- and bilayer
*region we find Vdc*(2−1)≈ 68 meV, which is very close to the

value reported above. However, other groups reported larger
*values of Vdc*(2−1) (Refs. 22 and 23), but as shown in the

following, this can be attributed to different doping, which
strongly depends on the preparation of the sample.29,30 _{The}
three closeups of Figs.3(e)and 3(f) (see white labeled 1.5 by
*1.5 μm boxes therein) will be discussed in Fig.*6.

The observed differences in work function compared to a
*multilayer area (N )S* are depicted in Fig.4 (full squares).

Compared to bulk graphite we observe a difference of 150,
82, and 26 meV, for single-, bi-, and three-layer graphene,
*respectively. The particularly large scattering of *(2)* _{S}* may

*be related to the relatively narrow bilayer region. The inset in*Fig.4shows the measured Raman G-line shift as a function

*of number of layers. The doping n of the sample can be*

*determined from the G-line position ωG*using the calculated

*relations n (ωG*) for single-layer31and bilayer graphene.32The

G-line shift is nearly symmetric and positive for electron

Number of layers N ΔΦ 1 2 3 4 5 6 1582 1583 1584 1585 1586 1587 1588 1589 nil -G p t ei sn oo i ) -1 m c( Number of layers N Exp. Raman G-line

Exp. Kelvin Probe x10 cm

FIG. 4. (Color online) Work function differences as a function of
the layer thickness (full squares), extracted by histogram analysis of
the acquired Kelvin probe data. (Inset) Raman G-line shift. Triangles
*indicate ab initio DFT calculations of the work functions for a doping*
*level of n =*−4.5× 1012_{cm}−2_{.}

and hole doping, therefore the sign of the doping cannot be
extracted from the measured G-line shift. However, assuming
*a hole doping on this flake, we find a doping level of n*≈
−(2.5 ± 1)× 1012_{cm}−2_{for the single-layer and n}_{≈ −(7.5 ±}
1.5)×1012_{cm}−2_{for the bilayer. Similar values can be obtained}*using the experimentally measured ωGas a function of n.*20,33,34

These Raman measurements suggest that single- and bilayer
graphene on the same sample have different doping values,
which will be further discussed below. For a number of layers
*larger than two, the analogous relation n (ωG*) has not been

determined yet.

**III. DENSITY FUNCTIONAL THEORY CALCULATION**
In order to compare the Kelvin probe measurements with

*ab initio DFT calculations, we used the PWscf code of*

*charge. Positive n corresponds to electron doping and negative*

*n*corresponds to hole doping. The surface charge density leads
to a discontinuity of the electric field across the graphene layers
*equal to σ/*0*, where *0 is the permittivity of the vacuum.
We assume that the counter charge density is located on the
bottom side of the system (e.g., in the gate electrode) such
**that the electric field is E***= σ/*0 below the graphene sheet
**and, assuming absence of adsorbates, we set E**= 0 above
the flake. The electric field configuration is reproduced in our
calculations by introducing monopole and dipole potentials
*in the edges of the super cell as described by Gava et al.*38
The resulting potential energy in the direction perpendicular
to the sheet is shown in Fig. 5(a) for single- and bilayer
graphene (a planar average in the directions parallel to the
sheets has been performed). The electric field is obtained from
the derivative of the planar average, calculated in the region
outside few-layer graphene where the potential energy is linear
**and E uniform. The zero electric field condition on the top**
*side of the system is required to define the work function S*,

which is the minimum energy for an electron to escape into
*vacuum. *_{∞} is the potential energy at infinite distance from
the system [in Fig.5(a), it is set to zero for convenience]. The
*work function S*of multilayer graphene is then defined as

*S= *∞*− F,* (1)

*where F*is the Fermi level.

In the insets of Fig. 5(a), we show the calculated band
structure for p-doped single- and bilayer graphene, around
the K point in the Brillouin zone (BZ). The effect of the
electric field on the system is twofold: (i) the band structure
is distorted and the alignment of the Dirac point is modified
with respect to the vacuum energy and (ii) the Fermi level
is shifted with respect to the Dirac point because of removal
or addition of charges. For the single layer, the electric field
*does not affect the linear crossing of the π bands (which is*
dictated by the hexagonal symmetry of the system). However,
for the bilayer the zero-field electric band structure displays a
*parabolic crossing of the π bands at K,*39_{and this crossing is}
lifted in presence of a finite electric field.

In Fig.5(b), we show the doping dependence of the work
*function S*of single and few-layer graphene, calculated with

Eq. (1), which includes both the effect of the Fermi level
shift due to the induced charge and the effect due to the
different screening properties of multilayer graphene. The
work function for single-layer graphene shows a strong doping
*dependence, while its variation in n decreases with increasing*
number of layers. This is due to the fact that the doping charge
(per unit area) can distribute over different layers. Thus, the
more layers there are, the lower is the Fermi level shift.

*The doping dependence of S* can be due to both, the

*variation of the Fermi level with respect to the Dirac point d*,

*or an electric-field-induced variation of d* with respect to the

vacuum level:

*S= (*∞*− d*)*+ (d− F),* (2)

*where d* *is calculated as the average energy of the π bands*

at K.40 _{For zero doping, our DFT calculations show that}
*(*∞*− d*) does not depend on the number of layers and it is

Planar a

v

er

age of potential ener

gy (eV ) Layer 1 Layer 2 cm ΦS cm εd εF

FIG. 5. (Color online) (a) Planar average of the potential
en-ergy across 1LG (dashed line) and 2LG (continuous line), for a
*doping value n= −4.5 × 10*12_{cm}−2_{, calculated in DFT. (Insets)}

Corresponding band structures of 1LG and 2LG around the K point,
*illustrating the difference in work function *1LG

*S* *for single- and *2LG*S*

for bilayer graphene. The planar average and band structures are
*plotted with respect to the energy in the vacuum *∞, here set to zero
*for convenience. (b) Ab initio DFT calculated work function, S*, as a

*function of doping concentration n, for multilayers graphene obtained*
from Eq. (1). The vertical dashed line indicates a doping value of
*n*= −4.5 × 1012_{cm}−2_{for which we found the best agreement with the}

*≈4.23 eV. Assuming that (*∞*− d*) is independent of the

doping:

*S≈ (d* *− F*)*+ 4.23 eV.* (3)

The comparison between Figs.5(b)and5(c)[i.e., Eqs. (2)
and (3)] shows that the approximated expression [Eq. (3)] well
reproduces the doping dependence of the work function for
*single-layer graphene. For the largest values of n considered*
in Fig. 5(c), the error in the work function difference with
*respect to n*= 0 is around 4%. Equation (3) also reasonably
reproduces the doping dependence of the work function for
bilayer graphene, even if in this case the error is increased
with respect to single-layer, being around 30%. In single- and
bilayer graphene, the work function is thus mainly determined
by the Fermi level shift with respect to the Dirac point as a
function of the charge density, justifying the analysis of Yu

*et al.*23 _{Our findings also explain a}√_{n}_{dependence of }

*S* on

the charge density for the single layer, and a linear dependence
*on n for the double layer. Indeed, for the single layer*

*d− F* *= −sign(n)*

√

*π¯hvF*

*|n|,* (4)

and for the biayer

*d− F* = −
*π¯h*2*n*

*2m*1

*,* (5)

*where vF* *is the Fermi velocity and m*1 is the effective mass.
Moreover, in our DFT calculations charges are adsorbed from
the bottom of the system. However, in the case of single- and
bilayer graphene, we have shown that the major effect which
determines the work function variation is the Fermi level shift
with respect to the Dirac point, i.e., the total doping charge

*n*, while the Dirac point shift with respect to the vacuum is
negligible. Therefore, from this decomposition, we conclude
that in the case of single- and bilayer graphene the work
function results to be independent of whether such charge
is adsorbed from the top or the bottom of the system. For more
than two layers, the error in the work function difference with
*respect to zero doping (n*= 0) becomes larger than in bilayer
graphene when using Eq. (3) and, therefore, the work function
cannot be interpreted as a simple shift in the Fermi energy.
In particular, one can notice that for a large number of layers
*the work function variation with n is negligible [Fig.* 5(b)],
because the graphene layers screen the electric field on the
bottom side of the sample. This screening is neglected in
Eq. (3) and therefore, for the comparison with experimental
results, we have used the work function values as calculated
in Eq. (1) and shown in Fig.5(b).

**IV. COMPARISON AND DISCUSSION**
**A. Layer dependent work function differences**

In Fig.4, we compare the experimentally observed work
function differences as a function of the layer thickness
*with the results of our ab initio DFT calculations. The*
*experimental results are in reasonable agreement with the ab*

*initio calculations when assuming an overall doping value of*
*n*= −4.5×1012_{cm}−2_{(see triangles and continuous line). We}
observe that the work function difference decreases
signifi-cantly for the first few-layers but it is no longer layer-dependent

for systems with more than four to five layers. This is in good
agreement with recent transport experiments on double-gated
few-layer graphene systems, where an interlayer screening
length of 1.2± 0.2 nm has been reported.41_{In contrast to the}
Kelvin probe data, we observe for the layer-dependent Raman
G-line position (see inset in Fig.4) a slight monotonic change
*even for larger layer numbers N. This is mainly attributed to the*
fact that interlayer screening does not play an important role
for the Raman measurement, since all layers are contributing
to the Raman signal. This is in contrast to the Kelvin probe
measurement, where the surface potential is playing the crucial
role and lower lying layers are partially screened. However
for very few-layer graphene samples (one to three layers),
where the doping-induced shift of the charge neutrality point
is the dominating mechanism for shifting the work function
difference (see discussion in Sec. III), the Raman data and
the Kelvin probe data are in reasonably good agreement. For
example, we observe an enhancement of the doping level of
the bilayer section in both data sets. The origin of this elevated
doping value is not known but it may be related to the relatively
small bilayer graphene area on the investigated sample, where
edge effects may play an important role, may also explain
the rather extended error bar. However, a systematic increased
doping level for bilayer graphene cannot be excluded, since
it could be in agreement with recent experimental results
on chemically functionalized graphene where it has been
found that adsorbates bind differently to single- and bilayer
graphene.42

From Fig.5(b), we can also notice that at the estimated
p-doping values (indicated by the vertical line), the small
*charging n*= 1.4 ×1011_{cm}−2 _{induced upon contact with}
the biased AFM tip only leads to a minor modification of the
*work functions, i.e., of V _{dc}*(2−1)as observed in our experiment
and mentioned above.

**B. Lateral variations in the work function of single- and**
**few-layer graphene**

20 mV 20 mV 1.7 nm

1.7 nm

pixel frequency (arb.units.) pixel frequency (arb.units.)

pixel frequency (arb.units.)

1LG

6LG

Topography Surface Potential Histograms

Surface Potential Fluctuations (mV)

20 mV 1.7 nm (a) (b) (c) SiO 2 (d) (e) (f) (g) (h) (i) −100 −5 0 5 10 50 100 150 200 −10 −5 0 5 10 0 20 40 60 80 −10 −5 0 5 10 0 20 40 60 80

FIG. 6. (Color online) Closeup views of topography (1.5 ×
*1.5 μm) and corresponding Kelvin probe data recorded on SiO*2

(a) and (d), 1LG (b) and (e), and 6LG (c) and (f) as indicated in
Figs.3(e)and 3(f). The topography images exhibit the presence of
contaminations, but do not show significant differences depending on
the layer thickness. The Kelvin probe measurements, in contrast, show
striking differences. Whereas the work function measured on 6LG is
very homogeneous, we see significant variations on 1LG, showing
that different substrate doping cannot be sufficiently screened. The
*width of the distribution δV _{dc}*(1)≈ 9 mV can be attributed to such local

*doping variations resulting in a charge inhomogeneity, while δVdc*(6)≈

3.6 mV lies in the range of the noise level of our KFM measurement setup. The variations are indicated by the corresponding histograms shown in panels (g) and (h).

partial screening of charge impurities that induce a doping. The corresponding histograms [Figs. 6(g) and 6(h)] show that single-layer graphene partially screens the impurities as expressed by a narrowing of the distribution in Fig.6(h). For single-layer graphene, we observe an asymmetric distribution of the surface potential as highlighted by the two arrows in Fig.6(h), whereas Figs.6(g)and6(i)exhibit a rather symmetric distribution. This asymmetry reflects the overall p-doping of the sample resulting in an excess of holes in the graphene

layer, which allows more efficient screening of electrons. Additionally, the linear density of states suppresses the screening of more positive charge impurities in the p-doped regime [see right arrow in Fig.6(h)]. Interestingly, we observe these strong variations in doping at elevated doping levels which consequently leads to the conclusion that significant disorder is also present at rather high carrier densities.

**V. CONCLUSION**

In summary, we presented Kelvin probe measurements on
single-, bi-, and few-layer graphene flakes resting on SiO2.
The Kelvin probe measurements revealed significant work
function variations as a function of the number of graphene
*layers, in quantitative agreement with ab initio DFT computed*
work functions for p-doped multilayer graphene. Moreover,
our calculations show that for single- and bilayer graphene the
work function variation with doping is mainly due to the shift
of the Fermi energy with respect to the Dirac point, while for
more than two layers the effects due to interlayer screening
become relevant and have to be carefully taken into account.
Measured and computed work function independently lead
to an interlayer screening length in the order of four to five
layers. The measurements, moreover, indicate different doping
values for single- and bilayer graphene on the same sample.
These findings are consistent with our Raman G-line shift
mea-surements. We observed significant variations of the surface
potential on 1LG. These variations are related to the partial
screening of charge impurities in the substrate which results
in a nonuniform charge density in graphene, and presently
*determine one of the major limitations in the performance of*
state-of-the-art graphene based electronic devices.

**ACKNOWLEDGMENTS**

The authors wish to thank D. Bishop, P. Brouwer, K. Ensslin, F. Guinea, T. Ihn, and R. W. Stark for helpful discussions and C. Hierold for providing access to the Raman spectrometer. Support by the ETH FIRST Lab and financial support by the Swiss National Science Foundation and NCCR Nanoscience are gratefully acknowledged. Calculations were performed at the IDRIS supercomputing center (Project No. 096128).

*_{Present address: Lawrence Berkeley National Laboratory, Molecular}

Foundry, 1 Cyclotron Road, Berkeley, California 94720, USA; dziegler@lbl.gov

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